Re-Fried Greenland Ice Cores

This is not going to be an especially interesting post for most (probably any) of you, but I want to document a couple of points mostly as an aide-memoire for myself so I don’t forget.

I actually learned something new about the Jones et al reconstruction from the Euro Team study. I’ve been able to sort of replicate the Jones study, but not to anything like adequate precision. Jones did not archive data as used, but did publish diagrams of the data and I used digital versions cobbled together elsewhere – mostly from MBH. Of the 17 proxies in the "independent" Jones study, 14 were used in MBH. After trying diligently, I asked Jones to provide me with the data as used and code. He refused. THe Euro Team has posted up digital versions of 5 Jones series, 4 of which were identical to the Mann versions. However, their Greenland version was somewhat different. It had a high correlation (0.75) but differed in detail. I’ve gone back and traced Mann’s version to Fisher’s veries DELNORM6.CVG, which is his "super-stack", including sites: Crete, A, B, C, D, H, Milcent, GISP2 and 4 GRID series, which I haven’t been able to identify.

The Jones version has a high correlation to a scaled composite of Crete, A,B, C, D, H and Milcent, but I couldn’t locate a precise equivalent in a detailed data set sent to me by Fisher, the author of the series.

Hegerl also uses a "decadally smoothed" version of this series, which is archived by the Euro Team (but not by herself.) She doesn’t state what the decadally smoothing is. I experimented with various gaussian filters, which are common in Team studies and got close but not exact. Eventually I determined that she used an 11-year running average. This filter applied to the Mann version yielded the Hegerl version – which was cut off in 1960 (though the original goes to 1983). Here is a plot of the 3 versions in the 20th century.

Figure 1. Three versions of West Greenland dO18.

As an experiment, I plotted up the data from the 7 cores which are said to be in the Crete stack, shown below. A couple of cores have values in 1984, which was not included in the composite. However the 1984 dO18 values appear to be the lowest values in the duration of the record (which starts in 553)

Figure 2. Twentieth Century Values of 7 Ice Cores in Crete, Greenland Area

As a reminder, here is a plot of the values over the entire series. This is remarkable for the uniformity of values. Fisher’s thoughts on this were that the sites were on a high plateau and were relatively unaffected by centennial changes in temperature.

5 Comments

AIG News will be publishing some articles on historical measured CO2 from air and sampling problems with ice-cores in Issue 86 due out in November 2006 plus some 11th hour French data on sampling methods

Re #2
It might be; but I don’t think 8 years of noisy decline is enough of a trend to conclude “divergence”. Also, that the decline is happening in the late 1970s, and not the late 1990s, suggests it is not nearly as divergent from the temperature record as some of the other cases that have been reported. But you’re right: this divergence problem is a devil. If tree ring responses to temperature are nonlinear, then that might lead to MWP temperature reconstructions that are biased low.

If you want to compare time series similarities, that is given a test target time series, say ‘A’, rank a collection of 4 time-series from the database (say, ‘B’, ‘C’, ‘D’, ‘E’) from the most similar ones to the most dis-similar ones. The popular algorithm for this is called ‘Dynamic Time Warping’ or DTW for short. DTW had been used in speech processing and signal processing in the past 20 years or so. So, if you want to rank your time-series from your graphs above and see which one is more similar to other ones, then look for DTW codes on the internet, which are freely available in Java, Matlab, etc…

You might be interested in NNMF (Non-negative Matrix Factorisation) algorithm where there are tons of Matlab codes available on the internet on NNMF. There are also tons of freely available papers on NNMF on the internet. NNMF is different from SVD (or PCA) factorisation in that it factorises a positive matrix (all elements), say ‘A’ into factor matrices which are also both positives. NNMF was originally developed for face-recognition but now it has exploded into other areas in signal processing, finance, search engine algorithm, image processing, recommendation engines (Amazon type, such as ‘Customer who bought item Q also look at item Z’), etc,…

PCA have got negative eigenvalues (hard to physically interpret) which are inappropriate for Mann’s temperature reconstruction. NNMF can help there, which it does not have negative factors.